Autonomous ground treatment appliances are generally designed to treat the ground using a treatment unit which is oriented parallel to the ground. By way of example, the blades of the mower mechanism of an autonomous robotic lawnmower are arranged parallel to the ground in order to uniformly cut the lawn. If the ground treatment appliance partly meets an obstacle or a wheel of the ground treatment appliance is on a step, this can lead to the treatment unit moving into an inclined position. Proper operation of the treatment unit cannot be ensured in this inclined position.